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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var constantFunction = require( '@stdlib/utils/constant-function' );
var degenerate = require( '@stdlib/stats/base/dists/degenerate/pdf' ).factory;
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var gamma = require( '@stdlib/math/base/special/gamma' );
var exp = require( '@stdlib/math/base/special/exp' );
var pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Returns a function for evaluating the probability density function (PDF) for a chi distribution with degrees of freedom `k`.
*
* @param {NonNegativeNumber} k - degrees of freedom
* @returns {Function} PDF
*
* @example
* var pdf = factory( 0.5 );
*
* var y = pdf( 2.0 );
* // returns ~0.04
*
* y = pdf( 1.0 );
* // returns ~0.281
*/
function factory( k ) {
var km1;
var kh;
if ( isnan( k ) || k < 0.0 ) {
return constantFunction( NaN );
}
if ( k === 0.0 ) {
return degenerate( 0.0 );
}
kh = k / 2.0;
km1 = k - 1.0;
return pdf;
/**
* Evaluates the probability density function (PDF) for a chi distribution with degrees of freedom `k`.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 1.0 );
* // returns <number>
*/
function pdf( x ) {
var out;
if ( isnan( x ) ) {
return NaN;
}
if ( x < 0.0 ) {
return 0.0;
}
out = pow( 2.0, 1.0-kh ) * pow( x, km1 ) * exp( -(x*x)/2.0 );
out /= gamma( kh );
return out;
}
}
// EXPORTS //
module.exports = factory;
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